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Abstract:
The imprint of non-linearities in the propagation of gravitational waves ---
the tail effect --- is responsible for new spin contributions to the energy
flux and orbital phasing of spinning black hole binaries. The spin-orbit
(linear in spin) contribution to this effect is currently known at leading
post-Newtonian order, namely 3PN for maximally spinning black holes on
quasi-circular orbits. In the present work, we generalize these tail-originated
spin-orbit terms to the next-to-leading 4PN order. This requires in particular
extending previous results on the dynamical evolution of precessing compact
binaries. We show that the tails represent the only spin-orbit terms at that
order for quasi-circular orbits, and we find perfect agreement with the known
result for a test particle around a Kerr black hole, computed by perturbation
theory. The BH-horizon absorption terms have to be added to the PN result
computed here. Our work completes the knowledge of the spin-orbit effects to
the phasing of compact binaries up to the 4PN order, and will allow the
building of more faithful PN templates for the inspiral phase of black hole
binaries, improving the capabilities of ground-based and space-based
gravitational wave detectors.